I NTRODUCTION TO L INEAR F UNCTIONS
W HAT DID WE LEARN ABOUT FUNCTIONS ? We spent the last unit discussing functions. We found the independent variable, __, the dependent variable, __, the __________, the ______, and the ________for the function. This unit we will be looking at a specific type of function – ___________________. x y equation table graph Linear Functions
S IMILARTIES Functions Linear Functions Differences: Both have tables. Both have graphs. Both have equations. Both have a domain and range Both have independent and dependent variables. Both can be continuous, the data is connected. Functions can be discrete, the data is not connected.
W HAT DOES A L INEAR F UNCTION LOOK LIKE ON A GRAPH ? A ________ __________ is a function that on a graph the solutions, ______, are represented by a _________ linear function (x,y)(x,y) line.
E XAMPLES OF FUNCTIONS : Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. Yes, it is a function. The graph is not a line. It is a nonlinear function.
E XAMPLES OF FUNCTIONS : Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. Yes, it is a function. The graph is not a line. It is a nonlinear function.
E XAMPLES OF FUNCTIONS : Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. No, not a function.
E XAMPLES OF FUNCTIONS : Is it a function? Then is it a linear or nonlinear function? No, not a function. Yes, it is a function. The graph is not a line. It is a nonlinear function.
E XAMPLES OF FUNCTIONS : Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is not a line. It is a nonlinear function. Yes, it is a function. The graph is not a line. It is a nonlinear function.
E XAMPLES OF FUNCTIONS : Is it a function? Then is it a linear or nonlinear function? No, not a function. Yes, it is a function. The graph is a line. It is a linear function.
E XAMPLES OF FUNCTIONS : Is it a function? Then is it a linear or nonlinear function? Yes, it is a function. The graph is a line. It is a linear function. Yes, it is a function. The graph is not a line. It is a nonlinear function.
V OCABULARY FOR LINEAR FUNCTIONS Linear function – function with a graph that is continuous Linear equation – equation whose graph is a straight line X intercept – the point where a line crosses the x axis of a graph Y intercept – the point where a line crosses the y axis Rate of change – how the steepness of a line is changing Slope – the steepness of the line on a graph
Slope formula – the formula used to find the slope between two ordered pairs Slope intercept form – y = mx + b – a form used to graph linear functions Point slope from – y – y 1 = m(x – x 1 ) Domain – the list of all x values Range – the list of all y values Independent variable – the input you choose for x Dependent variable – the output you get when you choose the input and apply the function rule
Function rule – the rule that defines the relationship between x and y
Positive slope – the line on a graph moves in an upward direction from left to right
Function rule – the rule that defines the relationship between x and y Positive slope – the line on a graph moves in an upward direction from left to right Negative slope – the line on a graph moves in a downward graph from left to right
Function rule – the rule that defines the relationship between x and y Positive slope – the line on a graph moves in an upward direction from left to right Negative slope – the line on a graph moves in a downward graph from left to right Zero slope – the slope of a horizontal line
Function rule – the rule that defines the relationship between x and y Positive slope – the line on a graph moves in an upward direction from left to right Negative slope – the line on a graph moves in a downward graph from left to right Zero slope – the slope of a horizontal line Undefined slope – the slope of a vertical line